34 citations · 185 across the 30 of their papers we have counts for
5 papers · 1 filter
Transversely affine foliations on projective manifolds
Gaël Cousin, Jorge Vitório Pereira
We describe the structure of singular transversely affine foliations of codimension one on projective manifolds X with zero first Betti number. Our result can be rephrased as a the…
The characteristic variety of a generic foliation
Jorge Vitorio Pereira
We confirm a conjecture of Bernstein-Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides th…
On the Poincare Problem for Foliations of General Type
Jorge Vitorio Pereira
Let F be a holomorphic foliation of general type on CP(2) which admits a rational first integral. We provide bounds for the degree of the first integral of F just in function of th…
Vector Fields, Invariant Varieties and Linear Systems
Jorge Vitorio Pereira
We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of suc…
Multiplicity of Invariant Algebraic Curves and Darboux Integrability
Jaume Llibre, Jorge Vitorio Pereira
We define four different kinds of multiplicity of an invariant algebraic curve for a given polynomial vector field and investigate their relationships. After taking a closer look a…